"The world is a complicated place, we are in close proximity to Russian Federation in Syria and other places, and I think it would be a very big mistake not to have open lines of communication", Paul said on Monday.
According to Russian state news agency RIA Novosti, Putin's press secretary Dmitry Peskov confirmed that the letter was sent to Putin "through diplomatic channels", but the Kremlin has not yet reviewed it.
The publication says that page is under the secrecy was in the editor from the Russians, who received them from officials in Russia and this Putin gave Trump.
"At Senator Paul's request, President Trump provided a letter of introduction".
The delivery of the letter comes just three weeks after the Helsinki summit between Trump and Putin that was pilloried by lawmakers on both sides of the aisle. While Trump obliged the senator and wrote the letter, the White House said the idea that Trump asked Paul to deliver the letter to Putin on Trump's behalf is not true.
The president has called special counsel Robert Mueller's investigation into possible ties between his campaign and Moscow a "witch hunt".
The president later corrected some of his remarks, saying he misspoke.
He also held talks in Moscow with parliamentarians and pledged to block new sanctions against Russian Federation.
Paul, a member of the Senate Foreign Relations Committee, has continued to meet with Russian officials in Moscow this week along with visiting the US embassy.
The two countries are also at odds over Syria and Ukraine.
The relationship has also created divisions within the administration. Putin's willingness to continue talks on nuclear weapon reductions as well as new limitations indicates an ongoing cooperation between the two nations, despite recent tensions.
The draft of the order viewed by the Post would allow the US government to impose sanctions on any foreign individual or entity that sticks their nose in a USA election.